
Fillin Numbers of Some Graphs
TANG Jiequan, SHU Jinlong
2006, 2006 (5):
7682.
By using the decomposition theorem and the local reductive elimination for the fillin of graphs, the fillin numbers of some special graphs, such as G_{1}×G_{2}, S(G) and double cyclic graphs were studied. And the following results were obtained: (1)F(P_{m}×P_{n})≦(m2)(n2), where m≧2, n≧2; ; (2) if G is a 2connected graph with m edges and n vertices, then F(S(G))=m+F(G); (3) let G be a double cyclic graph, the length of the two cycles being p and q, respectively, and t the number of the vertices which are both in the two cycles (the end points are excluded), then F(G)=p+qt6.
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